RENORMALONS IN ELECTROMAGNETIC ANNIHILATION DECAYS OF QUARKONIUM

We study the large-order asymptotic behavior of the perturbation serie s for short-distance coefficients in the NRQCD factorization formulas for the decays J/psi-->e(+)e(-) and eta(c)-->gamma gamma. The short-di stance coefficients of the leading matrix elements are calculated to a ll orders in the large-N-f limit. We find that there is a universal Bo rel resummable renormalon associated with the cancellation of the Coul omb singularity in the short-distance coefficients. We verify that the ambiguities in the short-distance coefficients from the first infrare d renormalon are canceled by ambiguities in the nonperturbative NRQCD matrix elements that contribute through relative order v(2). Our resul ts are used to estimate the coefficients of higher order radiative cor rections in the decay rates for J/psi-->e(+)e(-), eta(c)-->gamma gamma , and J/psi-->gamma gamma gamma.[S0556-2821(98)04407-5].